maths prob.bmp
Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.
Hope someone could help me out. Thanks.
maths prob.bmp
Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.
Hope someone could help me out. Thanks.
Think of the volume $\displaystyle V$ of water in the conical container as being composed of circular disks of thickness $\displaystyle dh$. We may then state:
$\displaystyle \frac{dV}{dt}=\pi r^2\frac{dh}{dt}$
We know the ratio of the radius of the water's surface to the height of the water level will be the same as that of the container:
$\displaystyle r=\frac{2}{3}h$ hence:
$\displaystyle \frac{dV}{dt}=\pi \left(\frac{2}{3}h \right)^2\frac{dh}{dt}$
Now, solve for $\displaystyle \frac{dh}{dt}$ and use the given values of $\displaystyle \frac{dV}{dt},h$ to compute the requested value.